Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}7x-y &= -2 \\ -5x+y &= -2\end{align*}$
Answer: Begin by moving the $x$ -term in the second equation to the right side of the equation. $y = {5x-2}$ Substitute this expression for $y$ in the first equation. $7x-({5x - 2}) = -2$ $7x - 5x + 2 = -2$ Simplify by combining terms, then solve for $x$ $2x + 2 = -2$ $2x = -4$ $x = -2$ Substitute $-2$ for $x$ back into the top equation. $7( -2)-y = -2$ $-14-y = -2$ $-y = 12$ $y = -12$ The solution is $\enspace x = -2, \enspace y = -12$.